|
Absolutely continuous probability measures. Measures defined by a density. The Radon-Nykodym theorem. Expectation under the new probability.
|
|
Random walk approximation of Brownian motion. Tree methods. Computationally simple trees: the case of a constant diffusion and the general case. How to parallelize the algorithm.
|
|
A general weak convergence result for diffusion processes. Monte Carlo simulation of a diffusion process: the Euler scheme. Discretization error and Monte Carlo error. How to parallelize the…
|
|
Brownian motion. Nondifferentiability of paths. The stochastic integral and the Ito isometry. Ito processes and Ito formula. Stochastic differential equations.
|
|
Markov chains: definition and examples. Simulation of a Markov chain. Simulation of Markov chains in the ergodic case.
|
|
Variance reduction methods in Monte Carlo: antithetic variables, control variates, importance sampling. Examples and implementation
|
|
Introduction to the course. Monte Carlo methods. Simulation of random variables. Error estimation with Monte Carlo methods.
|
|
Keynote Tuesday 27 June 09:00 ---- Explaining Success in Sports Competitions: Paired Comparison Methods with Explanatory Variables Speakers: Gerhard TutzProfessor em. at…
|
|
Keynote Monday 26 June 14:00 ---- Sports & Wellbeing with Technology & Data Speakers: Fabrizio Renzi:Direttore Tecnologia e Innovazione, IBM ItaliaPietro LeoExecutive Architect - IBM Italy…
|
|
Keynote Wednesday 28 June 14:00 ---- Mathematical models for sport: America's Cup, Olympic Rowing and more Speaker: Nicola ParoliniProfessor of Numerical Analysis at the MOX Laboratory -…
|